Speaker John Boehner gave House Republicans a presentation on Obamacare strategy at a closed-door meeting this morning that, while not ruling out the calls for the GOP to insist on defunding the health-care law when a government spending bill expires October 1, strongly suggested the House will be charting a different course.

“We’ve got a strategy,” Boehner told colleagues, according to a source in the room, adding:

This month has arguably been the most important moment in the three years since the law was signed. We passed bills to delay the employer mandate, and the individual mandate, the core of the law. Thirty-five Democrats defied the president and voted with us on Tim Griffin’s bill to authorize the delay of the employer mandate. Twenty-two Democrats defied the president and voted with us on Todd Young’s bill to delay the individual mandate. Former speaker Newt Gingrich called these votes “the beginning of the end” for Obamacare. We should view the delay votes this month as the opening salvo in a series of well-placed, targeted strikes that will ultimately dissolve the Obamacare coalition and topple this trainwreck of a law.

In the meeting, Boehner didn’t reject the possibility of making the next appropriations bill an all-or-nothing fight over Obamacare funding, and in a press conference afterwards he insisted “no decisions have been made.”

But the defunding strategy, championed by Senator Mike Lee and quickly embraced by many in the conservative movement, has received a fairly tepid response among House Republicans, even those on the right flank of the conference.

A good example is Representative Phil Roe of Tennessee. Roe is a doctor and chairman of the health care working group of the Republican Study Committee, the conservative caucus of the House Republicans. But he told me he wasn’t ready to sign on Lee’s CR strategy.

“I’m not there yet. I think that has a lot of ramifications . . . and I’d have to look at that with a jaundiced eye,” Roe said.

Others are more enthusiastic, and over 60 members have signed a letter from freshman representative Mark Meadows of North Carolina calling on House leadership to defund Obamacare through the appropriations process.

Looking ahead, Boehner told colleagues to expect a series of targeted votes that go after parts of the health care law that are particularly unpopular, such as the Independent Payment Advisory Board (IPAB). He also said the GOP will keep up the heat in terms of investigations about how the law is being implemented.